5.
The FLOW CONSULTANT
uniquely covers restrictive and critical flow meters. While
restrictive orifices and liquid Cavitating limiting flow-rate
devices are not flow meters they are widely used to limit or
provide a pressure loss (restriction) in a flow system.
Ans. The difference between
limiting flow and restricting flow are often misunderstood.
Critical (gas/vapor) or
Cavitating Liquid Flow: Gas Flow-rate is limited to a
fixed flow-rate for a given upstream pressure when a shock front is
created at the minimum flow area of the device, this is established
when the “Critical” pressure ratio is reached as the downstream
pressure is reduced. For air this occurs when the ratio of upstream
pressure to throat pressure is 0.53.
Liquid flow is limited when
the differential pressure equals the difference between upstream and
throat (or for an orifice) vena contracta pressure is the vapor
pressure of the fluid.
In both cases Bernoulli’s no
longer applies. For a thick orifice the overall pressure loss the
difference between the upstream pressure and the downstream
pressure. For a standardized critical flowmeter the pressure loss is
approximately 10 % of the choking difference between upstream and
downstream choking pressure.
Version 7
includes critical flow thick orifices, Torodial Throat and
Cylindrical Venturi.
Restrictive Orifices:
Restrictive orifices do not limit the flow but fix overall
pressure loss for a given flow rate. The FLOW CONSULTANT computes
the pressure loss using the standard orifice equation with the Stolz
derived discharge coefficient for pipe taps.
Pipe tap are located 2.5 pipe
diameters upstream of the plate and 8 pipe diameters downstream (2
1/2 and 8 D taps). This prediction equation well fits recent overall
pressure loss data (Miller p/ 6.41).
For gases a thin orifice plate
does not choke at the critical pressure ratio (see Figure below).
The gas expansion factor has a defined “bend” at the critical
pressure ratio (Miller, p 9.20). Cunningham’s equation for the gas
expansion factor is used in the flow consultant in this range.

Overall pressure loss for a
restrictive plate, used for sizing, is not the same as the pressure
drop across the plate. The FLOW CONSULTANT computes the
differential based on the corner tap pressure, as this is the actual
pressure difference across the plate. It is this differential that
is used in the Roark stress/strain equations to determine plate
thickness.
Multiple Plates: Often
a single orifice will not drop the required pressure at the desired
flow-rate. In this case multiple orifices are required. There is no
data for multiple plate spacing, however, it is reasonable to assume
pressure has 90 to 95% recovered after the eight (8) pipe diameters
and this be used as a spacing requirement between plates.
Estimated uncertainty:
It is estimated, based on the computational
|